一类非凸的不可定向交叉数的序列

It is well known that finding the crossing number of a graph on nonplanar surfaces is very difficult.In this paper we study the crossing number of the circular graph C（10,4） on the projective plane and determine the nonorientable crossing number sequence of C（10,4）.On the basis of the result,we show that the nonorientable crossing number sequence of C（10,4） is not convex.     

Number of Induced Matchings of Graphs

A matching M of a graph G is an induced matching if no two edges in M arejoined by an edge of G.Let iz(G) denote the total number of induced matchings of G,named iz-index.It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence.In this paper,we investigate the iz-index of graphs by using the Fibonacci-Narayana sequence and characterize some types of graphs with minimum and maximum iz-index,respectively.     

General Term of Sequence

In the study of number sequences,we learn to uncover how the sequence grows.Then we make a generalisation about the number sequence by stating the general term in algebraic form. Below is an activity using matches(or toothpicks,etc)to build and expand a number pattern. Given the pattern in the figures as follows:     

Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems

Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case.     

A Note on the Indirect Controls for a Coupled System of Wave Equations

By a procedure of successive projections, the authors decompose a coupled system of wave equations into a sequence of sub-systems. Then, they can clarify the indirect controls and the total number of controls. Moreover, the authors give a uniqueness theorem of solution to the system of wave equations under Kalman’s rank condition.     

A CLASS OF RANDOM NUMBER GENERATORS BASED ON WEYL SEQUENCE

The generation of good pseudo-random numbers is the base of many important fields in scientific computing, such as randomized algorithms and numerical solution of stochastic differential equations. In this paper, a class of random number generators （RNGs） based on Weyl sequence is proposed. The uniformity of those RNGs is proved theoretically. Statistical and numerical computations show the efficiency of the methods.     

二项序列的一个新的特征刻画

In this paper, a new characterization of the binomial sequence and its equivalent version are given. These characterizations are based on the joint conditional probability distribution of arrival times given that the number of arrivals occuring up to any fixed time is known. One application of these results is also explained.     

平面不可压缩的Navier-Stokes方程的一个新七模截断(英文)

A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.     

PROBABILITY MODEL OF GUNTHER GENERATOR

This paper constructs the probability model of Gunther generator at first,and the finite dimension union distribution of the output sequence is presented.The result shows that the output sequence is an independent and uniformly distributed 0,1 random variable sequence. It gives the theoretical foundation about why Gunther generator can avoid the statistic weakness of the output sequence of stop-and-go generator,and analyzes the coincidence between output sequence and input sequences of Gunther generator.The conclusions of this paper would offer theoretical references for designers and analyzers of clock-controlled generators.     

Packing Constant and Strong Extreme Point in Orlicz Spaces

Packing constant is an important and interesting geometric parameter.Packingconstant A_x of Banach space is a real number such that if r≤A_x,then a infinitenumber of spheres of radius r can be packed in the unit ball U(X),and if r>A_x,only a finite number of spheres can be done.It began in the 1950 studyingpacking constant of special sequence spaces.Rankin found A_2 and A_p of space l_2and l_p(p>1)respectively in 1955 and in 1958.In 1976,Cleaver discussed Orliczsequence space equipped with Orlicz norm [l_M, ||·||_M]·under a strong condition,     

Prime and composite numbers as integer parts of powers

We study prime and composite numbers in the sequence of integer parts of powers of a fixed real number. We first prove a result which implies that there is a transcendental number ξ>1 for which the numbers [ξ^{n !}], n =2,3, ..., are all prime. Then, following an idea of Huxley who did it for cubics, we construct Pisot numbers of arbitrary degree such that all integer parts of their powers are composite. Finally, we give an example of an explicit transcendental number ζ (obtained as the limit of a certain recurrent sequence) for which the sequence [ζⁿ], n =1,2,..., has infinitely many elements in an arbitrary integer arithmetical progression. This revised version was published online in June 2006 with corrections to the Cover Date.     

The odd-number sequence: squares and sums

Direct study of various characteristics of integers and their interactions is readily accessible to undergraduate students. Integers obviously fall in different classes of modular rings and thus have features unique to that class which can result in a variety of formations, particularly with sums of squares. The sum of the first n odd numbers is itself the square of n within the odd number sequence, from which testing for primality within the Fibonacci sequence is investigated in this note.     

Some double sequence spaces of interval numbers defined by Orlicz function

In this paper we introduce some interval valued double sequence spaces defined by Orlicz function and study different properties of these spaces like inclusion relations, solidity, etc. We establish some inclusion relations among them. Also we introduce the concept of double statistical convergence for interval number sequences and give an inclusion relation between interval valued double sequence spaces.     

有关调和数的更多渐近展开公式

基于指数型完全Bell多项式,建立了一个一般调和数渐近展开式,并给出展开式中系数的相应递推关系.由生成函数方法进一步推导出这些系数的具体表达式.另外,我们建立了两个在对数项里只含有奇数或偶数次幂项的lacunary调和数渐近展开式,     

Asymptotics in addition of pseudo-random sequences

The performance of individual pseudo-random sequence, generated by some mechanism, is often not ideal. The asymptotic performance of the addition (in the sense (mod ρ)) of a large number of such individual sequences is studied and the necessary and sufficient condition under which the resulting sequence may converge to genuine randomness is obtained. Project supported by the National Natural Science Foundation of China, the UPGC of Hong Kong, Hong Kong Baptist University and SRCU.     

Sequences of Ordered Sets and Catalan Numbers

We define the down sets (lower covers, respectively) sequence of an ordered set. We show that the number of down set sequences of an n-ordered set is equal to the n-th Catalan Number. We give a characterization of down sets sequences of an ordered set and another characterization of lower covers sequences of an ordered set.     

两两NQD列的强大数定律

该文把同分布的两两NQD列的Kolmogorov强大数定律推广到了在一类广泛的条件下的不同分布的情形, 为此而建立的Kolmogorov Chung型强大数定律本身也是有意义的.      

单调有界数列必有极限定理的一个直接证明及其作用

利用实数十进制无限小数表示直接构造性地给出"单调有界数列必有极限"定理的一种简洁的新证明,并且从新视角揭示数学分析中的实数完备性和高等数学中的数列极限存在准则.     

关于原数列及其均值

设p为素数,n为正整数,Sp(n)是其阶乘能被pn整除的最小正整数.本文研究了数列Sp(n)的均值性质,并给出了一个较强的渐进公式.     

A generalization of the formula for the triangular number of the sum and product of natural numbers

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of r natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.